In order to evaluate the effectiveness of a new type of plant food that was developed for tomatoes, a study was conducted in which a random sample of n = 72 plants received a certain amount of this new type of plant food each week for 14 weeks. The variable of interest is the number of tomatoes produced by each plant in the sample. The table below reports the descriptive statistics for this study: Descriptive statistics for the tomato food stud sample Variable n sample mean standard standard error deviation number\" 72 35.60 9.60 1.131 tomatoes Assuming the population is normally distributed, the investigators would like to construct a 98% confidence interval for the average number of tomatoes that all plants of this variety can produce when fed this supplement like this. a) The margin of error is: C] (3 decimals) b) The corresponding 98% confidence interval for the true population mean is: Lower Limit: (3 decimals) to Upper Limit: (3 decimals) c) What would we conclude at a = 0.02 for the hypothesis test Ho: M = 40.393 vs. Ha: M 40.393? 0 We do not have enough evidence to conclude the true mean is 40.393. 0 We do not have enough evidence to conclude the true mean is 35.60. 0 We have insufficient evidence to conclude the true mean is different from 40.393. Q We have enough evidence to conclude that the true mean is 40.393. 0 We have sufficient evidence to conclude that the true mean is different from 40.393. As part of its eco-friendly campaign, a company has asked for your advice whether installing a wind turbine will generate enough electricity to be cost effective. To produce enough electricity, the average wind speed needs to be least 16 mph. Based on historical data from the past 5 years, 45 days were randomly chosen and their wind speed measurements were written down. This resulted in an average wind speed of 17 mph with a standard error of 0.6559 mph. A histogram of these wind speeds yielded a right-skewed shape. (a) Are the conditions met for constructing a confidence interval? (Check all that apply.) C] None of the conditions are met. C] The days were randomly chosen. C] The Nearly Normal condition is met. C] It is reasonable to assume that weather conditions on the various days were independent of each other. (b) Find the 99% confidence interval for the true average wind speed. (Use 4 decimal places) ( I ) (c) Does the above confidence interval provide evidence that a wind turbine would be cost effective? 0 No, since the lower boundary is greater than the required wind speed of 16 mph, there is evidence the true average wind speed is greater than 16 mph. 0 No, since the lower boundary is less than the required wind speed of 16 mph, it is possible the true average wind speed is less than 16 mph. 0 Yes, since the lower boundary is greater than the required wind speed of 16 mph, there is evidence the true average wind speed is greater than 16 mph. 0 Yes, since the lower boundary is less than the required wind speed of 16 mph, it is possible the true average wind speed is less than 16 mph. In a certain region, 18% of people over age 50 didn't graduate from high school. We would like to know if this percentage is the same among the 25-30 year age group. Use critical values to exactly 3 decimal places. (a) How many 25-30 year old people should be surveyed in order to estimate the proportion of non-grads to within 4% with 95% confidence? (b) Suppose we wanted to cut the margin of error to 2%. How many people should be sampled now? (c) What sample size is required for a margin of error of 5%